At the moment you have a hypothesis that the issue is some sort of frost detection. You have not yet proved this hypothesis.
You originally said this noise started at 2am and stopped at 6am.
First experiment- change the system timer- advance it by 4 hours. Observe whether the noise still starts at 2am or starts at 6am.
Second experiment.
Acquire an indoor/outdoor thermometer (Aldi, £10). Place the outdoor detector near the outside unit.
Check that the only external components (sensors etc) are all in one location. If they are, acquire an electric fan heater and a long cable, lash up some rainproofing and point the fan heater at the external unit, about a metre away from it. Arrange it so you can switch fan heater on/off from inside the house.
When the pump racket starts, record the time and the outside temperature. Turn on the fan heater, observe and tecord time, the outside temperature and the racket status.
Experiment 3
Kit as above.
Turn the fan heater on at midnight (ie before the racket starts). Observe and record time, outside temp and racket status
In both above experiments, if outside temp doesn't rise when fan heater is on, move fan heater a bit closer to unit.
Random question. Do you have Evonomy 7 or any similar dual feed electricity supply? Do you ever observe occasional lights burning brighter/dimmer for a few seconds?